Building a Quadcopter

I am building a Quadcopter ,i am not sure how to decide(or calculate) the length of the 4 arms .I know that it depends on the propeller size ,i am not sure if any other parameters are involved ,is there any formula to find the length using the parameter(s)?

Is there any way to calculate the maximum speed of a Quadcopter theoretically? I know i can get the speed using the GPS system but is it possible to calculate it? can i get any links to some papers or something?

Ya know, aerospace engineering really is rocket science; it really is that hard!

i am talking about a quadcopter that is 1.5 feet in motor to motor distance(along the diagonal).
Other than simpler mechanical design and cost savings are there any other advantages of quadcopters over other UAVs? i read that helicopters are more stable as they don't need electronic stabilization which is required by quadcopter.

2.2 Rotation Matrix
To make a dynamic model, the forces and moments acting on the quadcopter must be found. The forces
must also be oriented so they influence the quadcopter in the correct way, no mater how quadcopter is
oriented. Gravity will always point the Z-direction of the navigation frame, but will have vector components
referred to the quadcopter dependent of its orientation. A vector can be oriented to any position with three
successive rotations. In order to overcome the gravity vector the quadcopter's orientation must be rotated,
but not in the physical way, to determine how much force the motors has to put out to keep it hoovering.
The rotations can be done one at a time.

I don't what they mean by 'overcoming gravity vector by rotating the orientation ,not in a physical way!!'can someone please explain?

Think of the quadcopter as a disk that can rotate in the plane, about it's axis. That disk can also be tilted by varying the balance of power between opposing motors. The orientation of the disk is important because it decides which motor combination needs power adjustment to navigate in a particular geographical direction. The quadcopter does not have to physically rotate to fly off in a different direction, it only needs to multiply it's orientation by the needed heading direction to decide which motors to adjust in power.

Any tilt from the horizontal will require an increase in thrust to maintain the magnitude of the vertical component that counters gravity. That can be computed by rotation of the orientation vector without physical rotation of the quadcopter.